I think I see some robot-hand here, and even though I'm not experienced with character-like attributes I'd say that you could think about it this way:
Anything that moves seperately should be detached, however, when something is one solid object I'd say to keep it attached together.

So I see this 1 finger connected to the main ball: The question to think about is: Is that finger welded to the ball in the design?
Yes: Keep it attached, it should be one single mesh as it would be in the real world.
No: Detach it, so that you can rotate / move it without affecting the ball

Sorry for not being clear , and yes, it is a robot and I was thinking that the fingers could move , but I do not know very well about rigging the character that is new to me . Then, later when I advance more I will show you this personal project , I would like to read your criticisms and things that could be improved .

I am putting into practice everything learned in the mech tutorial, any comment can help me and thank you for your time in answering me

If you want the fingers to be able to move/animate, you will need to rig them. but since they are mechanical hands. you can do this by putting dummy objects at every joint of the finger and linking the fingers to the dummy objects. The you can just animate the dummys. I'm posting a link to a video about rigging mechanical objects. Its a little more than what you are trying to do, but I think it will help you understand the rigging process a lot more.

I like the boolean operations overall, but it takes some extra work to clean it up a bit.
In addition, I think it would work easier to take a step back, start with less geometry and use Turbosmooth to establish the curvature.
I made a fairly similar shape (not same proportions and design, but I guess the info still can be implemented), here's a little step-by-step thing how I would approach it:

Note: When I made this I was focussing on the highpoly result, but still you can use the Turbosmooth to establish curvature for your lowpoly as well of course

1. I made a box, added 1 segment for each axis and modified the shape to match it a bit with the major proportions of the hip-design.

2. To establish curvature, I used a Turbosmooth modifier which results in:

3. Added a Edit Poly modifier on top; The Turbosmooth modifier provided me extra segments which I can use to create that hole.
I made a cylinder with 8 sides, this was my snapping-guide in order to move vertices of the actual model in place (using face/edge constraints so the shape doesn't deform that much):

4. From there, still using face constraint: I just started to inset & extrude some new geometry which will later be those seperate parts (the darker objects in the design).
Everything inside the red marked edges is what I added there:

5. From there I added more depth, and the actual hole in the body where you can eventually seperate these parts out by detaching if you like (for this example I just kept it together in 1 object).
I accidently added some support loops for highpoly stage already in the same edit poly...I advice not to make that mistake as well

6. After adding another edit poly with more support loops, a symmetry modifier and some Turbosmoothing, I ended up with something like this: